The documents listed below are incorporated herein by reference:    [1] J. L. Walker, “Range-Doppler Imaging of Rotating Objects,” IEEE Trans. on Aerospace and Electronic Systems, AES-16 (1), 23-52, (1980).    [2] D. E. Wahl, P. H. Eichel, D. C. Ghiglia, C. V. Jakowatz Jr., “Phase Gradient Autofocus—A Robust Tool for High Resolution SAR Phase Correction”, IEEE Transactions on Aerospace and Electronic Systems, Vol. 30, No. 3, pp. 827-834, July, 1994.    [3] C. V. Jakowatz Jr., D. E. Wahl, P. H. Eichel, D. G. Ghiglia, P. A. Thompson, Spotlight-Mode Synthetic Aperture Radar: A Signal Processing Approach, ISBN 0-7923-96774, Kluwer academic Publishers, 1996.    [4] W. G. Carrara, R. S. Goodman, R. M. Majewski, Spotlight Synthetic Aperture Radar Signal Processing Algorithms, ISBN 0-89006-728-7, Artech House, Inc., 1995.    [5] M. Denny, I. Scott, “Anomalous Propagation Limitations to High-Resolution SAR Performance”, Proceedings of the 2002 IEEE Radar Conference, Long Beach, Calif., USA, p. 249-254, 22-25 Apr. 2002.    [6] Bryan L. Burns, J. Thomas Cordaro, “Imaging synthetic aperture radar”, U.S. Pat. No. 5,608,404, Mar. 4, 1997.
Synthetic Aperture Radar (SAR) forms images of a scene by sampling energy from a scattered field along the radar's flight path and coherently processing the data. Coherence of the data set is facilitated by very accurately measuring the geometric relationship between the desired target scene and the radar's flight path, and accounting for this in the data processing. This requires measuring the radar's motion, or at least its relative motion, very accurately and with fractional-wavelength precision over the course of the synthetic aperture. Typically, an Inertial Measurement instrument is employed, and even this is often aided by Global Positioning Satellite navigation readings.
The raw SAR data is typically a two-dimensional array of complex data samples, with one dimension representing samples from echoes of individual pulses (fast-time), and the other dimension representing the pulse index number (slow-time). This collection is termed the phase history data. Since wideband modulation techniques, such as the Linear Frequency Modulated (LFM) chirp waveform, are normally used for individual pulses, the data needs to be processed, or compressed, in the intra-pulse or range direction to achieve the final desired range resolution. This is termed range-compression. The data needs further processing in the inter-pulse or azimuth direction to complete the image formation process. This is termed azimuth compression.
During the course of a synthetic aperture, as the radar's perspective towards a target scene changes, ranges to some target locations change or migrate relative to other target locations. This migration is deterministic and is compensated within the image formation process by algorithms such as the Polar Format Algorithm (PFA) developed by Walker (document [1] above).
Relatively small motion measurement errors manifest themselves principally as phase errors in the complex data samples, and if large enough become observable as a smearing, blurring, or other degradation in the image. For most SAR systems, however, the nature and degree of blurring is nearly identical in different parts of the degraded SAR image. This allows a measurement of the blurring function, and then a calculation of a suitable correction to be applied to the original data to compensate for the presumed motion error. Further processing then may yield a well-focused image devoid of the previously observable degradation. A number of algorithms exist to automatically focus the degraded image. While some measure and compensate blurring, others seek to optimize other measures, such as contrast ratio in the image. Collectively, these processes are termed “autofocus” algorithms. A very popular autofocus algorithm is the Phase Gradient Autofocus (PGA) algorithm described by Wahl, et. al. (document [2] above).
Very large relative motion measurement errors manifest themselves as an unexpected additional shifting or migration of target locations beyond the aforementioned deterministic migration during the course of the synthetic aperture. Degradation in images from data exhibiting errors of this magnitude are substantial, often rendering the image useless. Application of conventional autofocus techniques are unable to properly mitigate the image degradation.
A general presumption in the SAR community is that any motion measurement errors are less than the range resolution of the radar. Under this presumption, autofocus operations are conventionally applied to fully range-compressed images. Since autofocus typically requires iteratively processing the data into an image, efficiency is gained by repeating only the azimuth compression, and not the range compression operations. This presupposes that, for example, a radar with 2 cm nominal wavelength and 30 cm range resolution will never see more than (4π/λ) ρr=60π radians of phase error.
In addition to motion measurement errors, longer ranges impart greater deleterious atmospheric effects to the data, whereby electrical path lengths depart significantly from the physical path lengths. The electrical path length is related to the actual path length by the ratio of the average wavelength to the nominal wavelength, and accounts for atmospheric dielectric variations, refraction and other wave propagation phenomena. Since coherence depends on electrical path lengths, problematic errors similar to motion measurement errors may be induced by perturbations in the atmosphere's transmission characteristics in spite of perhaps otherwise adequate motion measurements.
While the presumption that apparent range errors are less than the radar's range resolution is often true, modern high-performance SARs can exceed this criterion. The drive for finer resolutions, longer ranges, and less expensive (and less accurate) motion measurement systems will increasingly cause situations where a target's echo return effectively exhibits a residual migration error exceeding one or more range resolution cells during the course of the synthetic aperture. This would doom to failure any autofocus scheme that presupposes otherwise, which includes autofocus schemes that operate only on fully range-compressed data. An example of this situation is illustrated by FIGS. 1 and 2. Initially, the re-sampled data is range-compressed as shown at R, and then azimuth-compressed as shown at A. These compression operations produce a complex image. As illustrated generally at 11, the average blurring function in the scene is measured, and it is assumed that this phenomenon is exclusively due to phase error. A phase correction vector that represents the inverse of the blurring function is applied to the range-compressed data 13, to de-convolve the blurring function. The resulting corrected range-compressed data 15 is then subjected to azimuth compression to re-form a more acceptably focused complex image at 17.
FIG. 2 illustrates the situation where a target's echo return exhibits a residual migration error that exceeds one or more range resolution cells during the course of the synthetic aperture. This is indicated generally at 23 in FIG. 2 by the irregularly shaped (not straight) configuration of the range-compressed data. Although the average blurring function in the scene can again be measured as indicated at 21, it is incorrect in this instance to assume that the blurring function is exclusively due to a phase error. A phase correction vector representing the inverse of the blurring function is applied to the range-compressed data to produce corrected range-compressed data at 25. After azimuth compression, the resulting complex image 27 is something other than an acceptably focused image, because the generation of the phase correction vector was constrained by the incorrect assumption that the range-compressed data at 23 is sufficiently “straight” (as was in fact the case in FIG. 1).
It is desirable in view of the foregoing to provide for correction of motion measurement errors that extend beyond the range resolution of a SAR. Exemplary embodiments of the invention can achieve this by effectively decreasing the range resolution of the SAR in order to permit measurement of the error. Other exemplary embodiments of the invention compare range profiles across the slow-time dimension in order to estimate the error. Once the error has been determined, appropriate frequency and phase correction can be applied to the uncompressed input data, after which range and azimuth compression can be performed to produce a desired SAR image.